The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

Solution

Physics sir · 3 steps

To emit a Balmer line the electron must fall to n = 2, so first lift it from n = 1 to at least n = 3.

1. What Balmer needs. Every Balmer line is a jump that ends on n = 2. The jump must start higher up, so the lowest starting level is n = 3.
2. Lift from ground. The atom begins in n = 1. The least energy it must absorb is the energy to reach n = 3, using Eₙ = -13.6/n² eV.

   Δ E = E₃ - E₁ = 13.6(1 - 1/9) eV = 12.09 eV

3. So. The minimum energy is about 12.1 eV, option (c). From n = 3 the electron can then drop to n = 2 and emit the first Balmer line.

The idea to keep. To get a line of any series, first ask which level the jump ends on, then lift the electron from the ground state to one level above it. That lift is the minimum energy.

Answer from the NTA final answer key. Solution by PrepWiser.